Hierarchical structure-and-motion recovery from uncalibrated images

This paper addresses the structure-and-motion problem, that requires to find camera motion and 3D struc- ture from point matches. A new pipeline, dubbed Samantha, is presented, that departs from the prevailing sequential paradigm and embraces instead a hierarchical approach. This method has several advantages, like a provably lower computational complexity, which is necessary to achieve true scalability, and better error containment, leading to more stability and less drift. Moreover, a practical autocalibration procedure allows to process images without ancillary information. Experiments with real data assess the accuracy and the computational efficiency of the method.Comment: Accepted for publication in CVI

Adaptive grid based localized learning for multidimensional data

Rapid advances in data-rich domains of science, technology, and business has amplified the computational challenges of Big Data synthesis necessary to slow the widening gap between the rate at which the data is being collected and analyzed for knowledge. This has led to the renewed need for efficient and accurate algorithms, framework, and algorithmic mechanisms essential for knowledge discovery, especially in the domains of clustering, classification, dimensionality reduction, feature ranking, and feature selection. However, data mining algorithms are frequently challenged by the sparseness due to the high dimensionality of the datasets in such domains which is particularly detrimental to the performance of unsupervised learning algorithms. The motivation for the research presented in this dissertation is to develop novel data mining algorithms to address the challenges of high dimensionality, sparseness and large volumes of datasets by using a unique grid-based localized learning paradigm for data movement clustering and classification schema. The grid-based learning is recognized in data mining as these algorithms are inherently efficient since they reduce the search space by partitioning the feature space into effective partitions. However, these approaches have not been successfully devised for supervised learning algorithms or sparseness reduction algorithm as they require careful estimation of grid sizes, partitions and data movement error calculations. Grid-based localized learning algorithms can scale well with an increase in dimensionality and the size of the datasets. To fulfill the goal of designing and developing learning algorithms that can handle data sparseness, high data dimensionality, and large size of data, in a concurrent manner to avoid the feature selection biases, a set of novel data mining algorithms using grid-based localized learning principles are developed and presented. The first algorithm is a unique computational framework for feature ranking that employs adaptive grid-based data shrinking for feature ranking. This method addresses the limitations of existing feature ranking methods by using a scoring function that discovers and exploits dependencies from all the features in the data. Data shrinking principles are established and metricized to capture and exploit dependencies between features. The second core algorithmic contribution is a novel supervised learning algorithm that utilizes grid-based localized learning to build a nonparametric classification model. In this classification model, feature space is divided using uniform/non-uniform partitions and data space subdivision is performed using a grid structure which is then used to build a classification model using grid-based nearest-neighbor learning. The third algorithm is an unsupervised clustering algorithm that is augmented with data shrinking to enhance the clustering performance of the algorithm. This algorithm addresses the limitations of the existing grid-based data shrinking and clustering algorithms by using an adaptive grid-based learning. Multiple experiments on a diversified set of datasets evaluate and discuss the effectiveness of dimensionality reduction, feature selection, unsupervised and supervised learning, and the scalability of the proposed methods compared to the established methods in the literature

Anytime Hierarchical Clustering

We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of nested partitions that satisfies a natural homogeneity requirement. Each recursive step re-edits the tree so as to improve a local measure of cluster homogeneity that is compatible with a number of commonly used (e.g., single, average, complete) linkage functions. As an alternative to the standard batch algorithms, we present numerical evidence to suggest that appropriate adaptations of this method can yield decentralized, scalable algorithms suitable for distributed/parallel computation of clustering hierarchies and online tracking of clustering trees applicable to large, dynamically changing databases and anomaly detection.Comment: 13 pages, 6 figures, 5 tables, in preparation for submission to a conferenc